What are my chances of getting into Phillips Exeter?

<p>I live in a really small town in the south of Mexico, and Exeter really caught my attention. I attend a private school, but I've been told by different teachers and psychologists that I should look for a school that is challenging for me, since I "have a great potential that I should take great advantage of", so I found Exeter, Choate and Middlesex. I'm applying for the three of them, but Exeter is definitely my favorite.
I have won seven national Maths competitions in the last few years, as well as receiving academic excellence in my current school every year, as well as in Ireland, where I studied 8th grade.
I have done my calculations relating to GPA with my current grades, getting a 4.00 as well as 92% score in SSAT sample tests.
I am a swimmer and play tennis.
Do you think I might have some chances of getting in?
I felt "connected" to these three schools, and I have read several testimonials as well as carefully studied the schools' websites, since this is EXTREMELY important for me. Unfortunately, I can't get this educational opportunities back home. </p>